一类非线性非局部扰动LGH方程的孤子行波解

冯依虎; 莫嘉琪

doi:10.3879/j.issn.1000-0887.2016.04.010

一类非线性非局部扰动LGH方程的孤子行波解

doi: 10.3879/j.issn.1000-0887.2016.04.010

冯依虎^1,2,
莫嘉琪²

¹亳州学院电子与信息工程系, 安徽亳州 236800;²安徽师范大学数学计算机科学学院, 安徽芜湖 241000

基金项目: 国家自然科学基金(40676016)；安徽省教育厅自然科学基金(KJ2015A347)；安徽省高校优秀青年人才支持重点项目(gxyqZD2016520)

详细信息

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.29
计量
- 文章访问数: 1076
- HTML全文浏览量: 71
- PDF下载量: 562
- 被引次数: 0
出版历程
- 收稿日期: 2015-08-12
- 修回日期: 2015-10-16
- 刊出日期: 2016-04-15

Soliton Travelling Wave Solutions to a Class of Nonlinear Nonlocal Disturbed LGH Equations

FENG Yi-hu^1,2,
MO Jia-qi²

¹Department of Electronics and Information Engineering,Bozhou College, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241000, P.R.China

Funds: The National Natural Science Foundation of China(40676016)

摘要

摘要: 利用经过改进的泛函分析变分迭代方法讨论了一类非线性非局部Landau-Ginzburg-Higgs（LGH）微分方程.首先，做行波变换, 引入泛函，并求出其变分，令其为0，得到了Lagrange(拉格朗日)算子应满足的条件，并求出它.然后, 引入一个经过改进的变分迭代式, 选取初始迭代函数为对应的无扰动LGH方程的孤子解.最后, 利用迭代式依次得到非线性非局部LGH扰动方程求出各次孤子行波的渐近解和LGH扰动方程的精确解.通过一个例子说明了用经过改进的泛函分析变分迭代方法得到求解是有效的方法.
- 行波 /
- 非线性 /
- 非局部
Abstract: A class of nonlinear nonlocal Landau-Ginzburg-Higgs (LGH) differential equations were discussed with the modified functional analytic variational iteration method. Firstly, a set of travelling wave transforms were constructed and the functional was introduced, of which the variation was determined and then was made equal to 0 to obtain the conditions for and solution of the Lagrange operator. Secondly, a modified variational iteration expression was employed and the soliton solutions to the corresponding non-disturbed LGH equations were selected as the initial iteration functions. Finally, all the asymptotic solutions and the exact solutions to the nonlinear nonlocal disturbed LGH equations were obtained, successively. From an example, the proposed modified functional analytic variational iteration method is proved valid and practicable.
- travelling wave /
- nonlinear /
- nonlocal

HTML全文

参考文献(31)

[1]	LIN Yi-hua, CENG Qing-cun. Kelvin waves in a simple air-sea coupled model in the tropics[J]. Progress in Natural Science, 1999,9(3): 211-215.
[2]	LIN Yi-hua, JI Zhong-zhen, ZENG Qing-cun. Meridional wind forced low frequency disturbances in the tropical ocean[J]. Progress in Natural Science, 1999,9(7): 532-538.
[3]	封国林, 戴新刚, 王爱慧, 丑纪范. 混沌系统中可预报性研究[J]. 物理学报, 2001,50(4): 606-611.(FENG Guo-lin, DAI Xin-gang, WANG Ai-hui, CHOU Ji-fan. On numerical predictability in the chaos system[J]. Acta Physica Sinica,2001,50(4): 606-611.(in Chinese))
[4]	潘留仙, 刘金龙, 李树深, 牛智川, 封松林, 郑厚值. InAs/GaAs单电子量子点量子比特的失相率[J]. 中国科学(A辑), 2002,32(6): 556-559.(PAN Liu-xian, LIU Jin-long, LI Shu-sen, NIU Zhi-chuan, FENG Song-lin, ZHENG Hou-zhi. Dephasing rate in a InAs/GaAs single-electron quantum dot qubit[J]. Science in China(Series A),2002,32(6): 556-559.(in Chinese))
[5]	McPhaden M J, Zhang D. Slowdown of the meridional overturning circulation in the upper Pacific Pcean[J]. Nature,2002,415(2): 603-608.
[6]	GU Dai-fang, Philander S G H. Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics[J]. Science,1997,275(7): 805-807.
[7]	刘式适, 付遵涛, 刘式达, 赵强. 一类非线性方程的新周期解[J]. 物理学报, 2002,51(1): 10-14.(LIU Shi-kuo, FU Zun-tao, LIU Shi-da, ZHAO Qiang. New periodic solutions to a kind of nonlinear wave equations[J]. Acta Physica Sinica,2002,51(1): 10-14.(in Chinese))
[8]	吴俊峰, 叶文华, 张维岩, 贺贤土. 二维不可压流体瑞利-泰勒不稳定性的非线性阈值公式[J]. 物理学报, 2003,52(7): 1688-1693.(WU Jun-feng, YE Wen-hua, ZHANG Wei-yan, HE Xian-tu. Nonlinear threshold of two-dimensional Rayleigh-Taylor growth for incompressible liquid[J]. Acta Physica Sinica,2003,52(7): 1688-1693.(in Chinese))
[9]	王林山, 徐道义. 变时滞反应扩散Hopfield神经网络的全局稳定性[J]. 中国科学(E辑), 2003,32(6): 488-495.(WANG Lin-san, XU Dao-yi. Global stability for reaction diffusion Hopfield neural network with variable time delay[J]. Science in China(Series E), 2003,32(6): 488-495.(in Chinese))
[10]	潘留仙, 左伟明, 颜家壬. Landau-Ginzburg-Higgs方程的微扰理论[J]. 物理学报, 2005,54(1): 1-5.(PAN Liu-xian, ZUO Wei-ming, YAN Jia-ren. The theory of the perturbation for Landau-Ginzburg-Higgs equation[J]. Acta Physica Sinica,2005,54(1): 1-5.(in Chinese))
[11]	MO Jia-qi, ZHU Jiang, WANG Hui. Asymptotic behavior of the shock solution for a class of nonlinear equations[J]. Progress in Natural Science,2003,13(10): 768-770.
[12]	MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China(Series A),1989,32(11): 1306-1315.
[13]	莫嘉琪, 张伟江, 何铭. 非线性广义Landau-Ginzburg-Higgs方程孤子解的变分迭代解法[J]. 物理学报, 2007,56(4): 1847-1850.(MO Jia-qi, ZHANG Wei-jiang, HE Ming. The variational iteration method for the soliton solution of nonlinear generalized Landau-Ginzburg-Higgs equation[J]. Acta Physica Sinica,2007,56(4): 1847-1850.(in Chinese))
[14]	莫嘉琪, 陈秀. 非线性广义LGH方程的孤子近似解[J]. 兰州大学学报(自然科学版), 2008,44(3): 109-112.(MO Jia-qi, CHEN Xiu. Approximate solution to soliton for nonlinear generalized LGH equation[J]. Journal of Lanzhou University(Natural Sciences),2008,44(3): 109-112.(in Chinese))
[15]	MO Jia-qi, LIN Wan-tao, WANG Hui. A class of homotopic solving method for ENSO model[J].Acta Mathematica Scientia,2009,29(1): 101-110.
[16]	MO Jia-qi. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J].Science in China Series G: Physics, Mechanics and Astronomy,2009,52(7): 1007-1010.
[17]	MO Jia-qi, LIN Wan-tao, LIN Yi-hua. Approximate solution for mechanism of thermally and wind-driven ocean circulation[J].Chinese Geographical Science,2010,20(5): 383-388.
[18]	MO Jia-qi, LIN Wan-tao, LIN Yi-hua. Asymptotic solution for the El Nino time delay sea-air oscillator model[J].Chin Phys B,2011,20(7): 070205.
[19]	MO Jia-qi. Solution of travelling wave for nonlinear disturbed long-wave system[J].Communications in Theoretical Physics,2011,55(3): 387-390.
[20]	MO Jia-qi, LIN Yi-hua, LIN Wan-tao, CHEN Li-hua. Perturbed solving method for interdecadal sea-air oscillator model[J].Chinese Geographical Science,2012,22(1): 42-47.
[21]	FENG Yi-hu, MO Jia-qi. The shock asymptotic solution for nonlinear elliptic equation with two parameters[J]. Math Appl,2015,27(3): 579-585.
[22]	FENG Yi-hu, LIU Shu-de. Spike layer solutions of some quadratic singular perturbation problems with high-order turning points[J].Math Appl,2014,27(1): 50-51.
[23]	冯依虎, 石兰芳, 汪维刚, 莫嘉琪. 一类广义非线性强阻尼扰动展方程的行波解[J]. 应用数学和力学, 2015,36(3): 315-324.(FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, MO Jia-qi. Travelling wave solution to a class of generalized nonlinear strong-damp disturbed evolution equations [J].Applied Mathematics and Mechanics,2015,36(3): 315-324.(in Chinese))
[24]	冯依虎, 石兰芳, 许永红, 莫嘉琪. 一类大气尘埃等离子体扩散模型研究[J]. 应用数学和力学, 2015,36(6): 639-650.(FENG Yi-hu, SHI Lan-fang, XU Yong-hong, MO Jia-qi. Study on a class of diffusion models for dust plasma in atmosphere[J].Applied Mathematics and Mechanics,2015,36(6): 639-650.(in Chinese))
[25]	HE Ji-huan, WU Guo-cheng, Austin F. The variational iteration method which should be followed[J]. Nonlinear Science Letters A—Mathematics, Physics and Mechanics, 2010,1(1): 1-30.
[26]	WANG Qi, FU Feng-lian. Variational iteration method for solving differential equations with piecewise constant arguments[J].International Journal of Engineering and Manufacturing,2012,2(2): 36-43.
[27]	黄念宁. 孤子理论和扰动方法[M]. 上海: 上海科技教育出版社, 1996.(HUANG Nian-ning. Theory of Solitons and Method of Perturbations[M]. Shanghai: Shanghai Scientific and Technological Education Publishing House, 1996.(in Chinese))
[28]	PAN Liu-xian, YAN Jia-ren, ZHOU Cuang-hui. Direct approach for soliton perturbations based on the Green’s function[J].Chinese Physics,2003,10(7): 594-598.
[29]	范恩贵, 张鸿庆. 非线性波动方程的孤波解[J]. 物理学报, 1997,46(7): 1254-1258.(FAN En-gui, ZHANG Hong-qing. The solitary wave solutions for a class of nonlinear wave equations[J].Acta Physica Sinica, 1997,46(7): 1254-1258.(in Chinese))
[30]	de Jager E M, JIANG Fu-ru. The Theory of Singular Perturbation [M]. Amsterdam: North-Holland Publishing Co, 1996.
[31]	Barbu L, Morosanu G. Singularly Perturbed Boundary-Value Problems [M]. Basel: Birkhauserm Verlag AG, 2007.

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 1076
HTML全文浏览量: 71
PDF下载量: 562
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

一类非线性非局部扰动LGH方程的孤子行波解

doi: 10.3879/j.issn.1000-0887.2016.04.010

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

Soliton Travelling Wave Solutions to a Class of Nonlinear Nonlocal Disturbed LGH Equations

计量

目录

留言板

一类非线性非局部扰动LGH方程的孤子行波解

doi: 10.3879/j.issn.1000-0887.2016.04.010

作者简介: 冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Soliton Travelling Wave Solutions to a Class of Nonlinear Nonlocal Disturbed LGH Equations

计量

出版历程

目录

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).